Question
System is shown in the figure. Assume that cylinder remains in contact with the two wedges. The velocity of cylinder is –
The correct answer is: ![square root of 7 u m divided by s](data:image/png;base64,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)
Related Questions to study
Let
, then which of the following is true?
Let
, then which of the following is true?
For all twice differentiable functios
, with ![f left parenthesis 0 right parenthesis equals f left parenthesis 1 right parenthesis equals f to the power of ´ end exponent left parenthesis 0 right parenthesis equals 0](data:image/png;base64,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)
For all twice differentiable functios
, with ![f left parenthesis 0 right parenthesis equals f left parenthesis 1 right parenthesis equals f to the power of ´ end exponent left parenthesis 0 right parenthesis equals 0](data:image/png;base64,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)
The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle should be :–
The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle should be :–
A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given by :–
A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given by :–
Let
be a twice differentiable function on
. If
,
and
, for all
, then ![colon](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAYAAAAKCAYAAACXDi8zAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAABZJREFUeNpjYECA/ww4AE6JAQUUOhcAJvAD/V1ni1wAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPjo8L21vPjwvbWF0aD5NP229AAAAAElFTkSuQmCC)
Let
be a twice differentiable function on
. If
,
and
, for all
, then ![colon](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAYAAAAKCAYAAACXDi8zAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAABZJREFUeNpjYECA/ww4AE6JAQUUOhcAJvAD/V1ni1wAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPjo8L21vPjwvbWF0aD5NP229AAAAAElFTkSuQmCC)
A insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the surface and the insect is . If the line joining the centre of the hemispherical surface to the insect makes an angle a with the vertical, the maximum possible value of
is given :
A insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the surface and the insect is . If the line joining the centre of the hemispherical surface to the insect makes an angle a with the vertical, the maximum possible value of
is given :
A long horizontal rod has a bead which can slide along its length and is initially placed at a distance L from one end A of the rod. The rod is set in angular motion about A with a constant angular acceleration, . If the coefficient of friction between the rod and bead is , and gravity is neglected, then the time after which the bead starts slipping is
A long horizontal rod has a bead which can slide along its length and is initially placed at a distance L from one end A of the rod. The rod is set in angular motion about A with a constant angular acceleration, . If the coefficient of friction between the rod and bead is , and gravity is neglected, then the time after which the bead starts slipping is
A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are equal to each other, and no energy is lost when particle changes direction from PQ to QR. The values of the coefficient of friction
and the distance x(=QR), are, respectively close to:
A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are equal to each other, and no energy is lost when particle changes direction from PQ to QR. The values of the coefficient of friction
and the distance x(=QR), are, respectively close to:
An observer can see through a pin–hole the top end of a thin rod of height h, placed as shown in the figure. The beaker height is 3h and its radius h. When the beaker is filled with a liquid up to a height 2h, he can see the lower end of the rod. Then the refractive index of the liquid is
![](data:image/png;base64,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)
An observer can see through a pin–hole the top end of a thin rod of height h, placed as shown in the figure. The beaker height is 3h and its radius h. When the beaker is filled with a liquid up to a height 2h, he can see the lower end of the rod. Then the refractive index of the liquid is
![](data:image/png;base64,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)
A diverging beam of light from a point source S having divergence angle a, falls symmetrically on a glass slab as shown. The angles of incidence of the two extreme rays are equal. If the thickness of the glass slab is t and the refractive index n, then the divergence angle of the emergent beam is
![](data:image/png;base64,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)
A diverging beam of light from a point source S having divergence angle a, falls symmetrically on a glass slab as shown. The angles of incidence of the two extreme rays are equal. If the thickness of the glass slab is t and the refractive index n, then the divergence angle of the emergent beam is
![](data:image/png;base64,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)
A rectangular glass slab ABCD, of refractive index n1, is immersed in water of refractive index
A ray of light in incident at the surface AB of the slab as shown. The maximum value of the angle of incidence amax, such that the ray comes out only from the other surface CD is given by
![](data:image/png;base64,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)
A rectangular glass slab ABCD, of refractive index n1, is immersed in water of refractive index
A ray of light in incident at the surface AB of the slab as shown. The maximum value of the angle of incidence amax, such that the ray comes out only from the other surface CD is given by
![](data:image/png;base64,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)
A smooth block is released at rest on a incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is-
A smooth block is released at rest on a incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is-
A block is kept on a friction less inclined surface with angle of inclination . The incline is given an acceleration a to keep the block stationary. Then a is equal to-
A block is kept on a friction less inclined surface with angle of inclination . The incline is given an acceleration a to keep the block stationary. Then a is equal to-